Phase rotation watermarking for phase modulation

ABSTRACT

A method of generating a phase modulated signal includes generating a sequence of phase modulated host symbols having continuous, antipodal phase transitions between adjacent ones of the host symbols representing different states, and generating a sequence of overlay symbols each spanning a respective set of the host symbols. The method further includes rotating the continuous, antipodal phase transitions between the adjacent ones of the host symbols in each set of the host symbols in a same rotation direction according to a symbol state of the respective overlay symbol spanning the set of the host symbols, and generating a phase modulated transmit signal that conveys the continuous, antipodal phase transitions rotated according to the symbol states of the overlay symbols. For M-ary PSK, the method further includes encoding both antipodal and non-antipodal host symbol phase shifts to carry the data of the overlay symbols.

BACKGROUND

There is a pressing need to increase the amount and/or different typesof information that communication and navigation systems can transmit,without appreciably degrading the frequency spectrum associated with thetransmitted information. For example, widening of the frequency spectrumand shallowing of frequency nulls within the frequency spectrum shouldbe avoided. Such information includes, but is not limited toauthentication information. Authentication may be used to identifyequipment, such as transmitters and receivers, and various signals usedin the communication and navigation systems. Authentication methods havebeen proposed for Global Positioning System (GPS) signals to combat“spoofing” attacks that inject false signals. The authentication methodsenable a GPS receiver to determine that a GPS navigational waveformreceived by the receiver is legitimate. One such method proposes tooverlay a known “watermark message” on the GPS navigational waveformtransmitted from a space vehicle or other GPS broadcast platform. Suchwatermarking must not impact compliance with the baseline GPSnavigational waveform. Methods have also been proposed to overlay anadditional data channel or watermark onto a “host” data communicationlink. Whether the host is a navigational waveform or a datacommunication channel, the overlaid watermark or data channel shouldcause minimal degradation to the demodulated host waveform performancewhile providing enough energy to communicate the watermark or datamessage in weak signal or challenged environments such as urbanmultipath and jamming. The watermarking should minimize impacts on bothtransmitter and receiver complexity. Conventional approaches to providesuch watermark overlays for GPS and general data links meet thesecriteria only to a limited extent in that there is still significantdegradation to the underlying host waveform in order to provide a robustwatermark or data overlay.

SUMMARY

An embodiment presented herein is directed to a method of superimposinga watermark or overlay data channel, hereafter referred to as the“overlay,” onto a baseline or “host” phase modulated transmit signal.The method includes generating a sequence of binary phase modulated(BPSK) host symbols such that there are continuous, antipodal phasetransitions between adjacent host symbols representing different states,while superimposing a sequence of overlay symbols each spanning a set ofmultiple host symbols. The method further includes rotating thecontinuous, antipodal phase transitions in each set of the host symbolsin a same rotation direction according to a symbol state of therespective overlay symbol spanning the set of the host symbols, andgenerating a phase modulated transmit signal that conveys thecontinuous, antipodal phase transitions rotated according to the symbolstates of the overlay symbols. Rotating the phase transitions isreferred to as phase rotation watermarking and has the effect ofsuperimposing the overlay symbols (also referred to as additional data)onto the phase modulation of the host waveform.

Another embodiment presented herein is directed to a receiver. Thereceiver includes a radio frequency (RF) front-end to receive an RFsignal and frequency down-convert the RF signal to a down-convertedsignal. The RF signal and the down-converted signal each conveys (i) asequence of phase modulated host symbols having continuous, antipodalphase transitions between adjacent host symbols representing differentstates, and (ii) a sequence of overlay symbols each spanning arespective set of the host symbols in time, wherein the continuous,antipodal phase transitions in each set of the host symbols are rotatedin a same direction according to an overlay symbol state of therespective overlay symbol spanning the set of host symbols. The receiveralso includes a first demodulator to demodulate the host symbols fromthe down-converted signal, and a second demodulator to demodulate theoverlay symbols from the down-converted signal.

Though not strictly required, in certain implementations, the phaserotation watermarking can be incorporated into a constant envelope,constant phase modulation signal, which is a preferred method to achievehigh RF/Direct Current (DC) efficiency with saturated amplifiers, whilereducing the bandwidth of a transmitted signal produced using themodulations. These modulations also have low peak to average power ratio(PAPR) which results in higher power output and reduced multipactionrisk since the peak power is reduced.

The proposed invention can also be applied to a non-constant envelopeCPM, such as regular BPSK. In that case, the watermarking guides phasetransition in a trajectory that does not go through the origin, but theoverall phase trajectory may not be a circle as shown in FIGS. 2-4,discussed below, but rather an ellipse, with a brief, lower amplitudepulse on a Q channel during the phase transitions. Such watermarkingadds a small amount of extra energy, which is applied only during thephase transitions. Like the constant envelope case, the phase ramp slopepolarity can be accumulated over a large number of host symbols toprovide robustness.

With Binary CPM (BCPM) signals, the phase trajectory between symbols maybe either in the Clockwise (CW) or counterclockwise (CCW) directionwithout affecting the transmitted information. The phase rotationwatermarking exploits the BCPM phase trajectories to overlay a channelof data (the additional/overlay data) onto the host waveform withoutimpacting the performance of the host waveform. Since the host waveformnormally transitions between antipodal phase states, encoding thedirection of these phase transitions with additional data is a way ofusing otherwise wasted energy.

The phase rotation watermarking may also be applied to M-ary CPM whereM>=4. In this case, the phase rotation watermarking may exploit only thesubset of phase transitions in the M-ary CPM waveform that areantipodal.

Applications include, but are not limited to, phase rotationwatermarking for authentication, overlaying an additional data channel,or superimposing a coarse acquisition signal onto a precise acquisitionsignal so that both can be sent over the same waveform with little or noadditional power.

The above and still further features and advantages of the describedsystem will become apparent upon consideration of the followingdefinitions, descriptions and descriptive figures of specificembodiments thereof wherein like reference numerals in the variousfigures are utilized to designate like components. While thesedescriptions go into specific details, it should be understood thatvariations may and do exist and would be apparent to those skilled inthe art based on the descriptions herein.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an example communication or navigationsystem in which a phase modulation technique referred to as “phaserotation watermarking” may be implemented to superimpose additional dataon a host waveform.

FIG. 2 illustrates two phase trajectory options (clockwise andcounter-clockwise) for phase rotation transitions between two symbolphases that are 180° apart in an antipodal phase modulation schemeinvolving continuous phase transitions.

FIG. 3 illustrates an antipodal phase trajectory with a fixed, positive(counter-clockwise) phase rotation polarity for all transitions betweenthe two symbol phases.

FIG. 4A illustrates an antipodal phase trajectory with an alternatingphase rotation polarity for transitions between the two symbol phases.

FIG. 4B illustrates a host Q-ary CPM constellation showing two possiblephase transitions for a 90 degree host symbol shift, allowingwatermarking to be applied for non-antipodal adjacent symbol states.

FIG. 5 is a time-domain graph showing how phase rotation watermarkingcontrols rotational phase polarities of continuous phase transitions fora host signal according to an overlay signal.

FIG. 6A is a block diagram of an example modulation system capable ofimplementing phase rotation watermarking.

FIG. 6B is a block diagram illustrating of another exampleimplementation of an RF modulation system capable of implementing phaserotation watermarking.

FIG. 7A is a time-domain graph illustrating an example phase trajectoryhaving a series of positive rotation phase transitions between antipodalstates over several symbols for a Gaussian filtered phase trajectory CPMBOC(10,5) waveform.

FIG. 7B is a time-domain graph illustrating the same phase trajectory asFIG. 7A over several, R, symbol intervals in a phase rotation polaritypattern, where the phase rotation polarity is constant (either positiveor negative) within each R symbol interval.

FIG. 7C is a signal vector scatterplot diagram for the same waveformshown in FIGS. 7A and 7B.

FIG. 7D is a frequency-domain graph illustrating the power spectrum ofthe waveform of FIGS. 7A-7C compared with a reference binary phase shiftkeying (BPSK) BOC(10,5) waveform.

FIG. 7E is a graph illustrating the cross correlation of the waveform ofFIGS. 7A-7D compared with the reference BPSK BOC(10,5) waveform.

FIG. 7F is a frequency domain graph illustrating the output spectrum ofa saturated high power RF amplifier using the waveform of FIGS. 7A-7Ecompared with the reference BPSK BOC(10,5).

FIG. 8 is a block diagram of another implementation of a modulationsystem capable of implementing phase rotation watermarking.

FIG. 9 is a block diagram of an example receiver capable of demodulatinga phase modulated host waveform and demodulating phase rotationmodulation of additional data overlaying the host waveform.

FIG. 10 is a block diagram of an example phase rotation watermarkingdemodulator.

DETAILED DESCRIPTION

Embodiments presented herein employ a phase modulation techniquereferred to as “phase rotation watermarking,” “rotation watermarking,”or “phase rotation modulation” to superimpose additional (overlay)data/information on continuation phase modulation of a host waveform.The superimposed additional data is also referred to herein as a“watermark” or “watermark data.” Phase rotation watermarking provides asimple, robust, hard to detect, method of using the host waveform ordata stream to carry the additional data without degrading transmissionperformance. Phase rotation watermarking exploits the inherent phasetrajectory rotation between antipodal symbols of a binary phase shiftkeying (BPSK), quadrature phase shift keying (QPSK), M-ary phase shiftkeying (MPSK), or other phase modulated host waveform to carry theadditional data. When the host waveform transitions between its adjacentsymbols which are antipodal (180 degrees apart) there are two directionsthe phase trajectory can take, either clockwise or counter-clockwise.Phase rotation watermarking uses these two direction possibilities tocarry the additional information. For M>=4, it is also possible toencode non-antipodal host symbol phase shifts to carry the overlaysymbol phase rotation information. It can also be applied to modulationssuch as QAM, as will be described below. Phase rotation watermarkingrequires less hardware complexity than many of the other methods in use.For continuous phase modulation systems, minimal changes are needed tothe modulator hardware as the phase rotation is already being generatedby the modulation. Also, the embodiments offer the system designer morecontrol over the transmitted waveform, as will be described below.

As used herein and in the claims, the term “symbol” refers to a timeinterval of a signal in which the signal has a symbol state (alsoreferred to as a “symbol state value” or simply “symbol value”), or inwhich the phase of the signal is in a state representing some symbolvalue/symbol state. In the case of a spread spectrum signal in which aspreading code such as a pseudonoise (PN) code is used to spread aninformation signal, each “chip” of the PN code is a “symbol” within themeaning used herein (which would be distinct from a data symbol thatcould be represented by a sequence of such PN chips in this content).

As used herein and in the claims, the term “pattern” refers to a timesequence of symbols or symbol values in some order that can be, forexample, random, indeterminate, pseudo-random or semi-random, based on apseudo-noise code, fixed or predetermined, weighted towards certainvalues, and combinations thereof.

With reference to FIG. 1, there is shown a block diagram of acommunication or navigation system 100 that employs phase rotationwatermarking to increase the amount and and/or different types ofinformation transmitted by the system. System 100 includes a transmitter(TX) 102 and a receiver (RX) 104. Transmitter 102 receives a host signal106 (also referred to as a “host waveform”) including a sequence of hostsymbols (also referred to as “host symbols”). Transmitter 102 alsoreceives an overlay signal 108 (also referred to as “additional data”)including a sequence of overlay symbols (also referred to as “overlaysymbols”). Host signal 106 may be a navigation signal, such as a GPScode, although other signals are possible. Overlay signal 108 mayinclude a predetermined sequence of overlay symbols representative of anauthentication sequence or watermark, or may include an indeterminatesequence of overlay symbols from a data source (not shown in FIG. 1).

At a high-level, transmitter 102 uses phase rotation watermarking togenerate a continuous phase modulated transmit signal 110 that conveysphase information representative of both host signal 106 and overlaysignal 108. Transmitter 102 transmits transmit signal 110 to receiver104. Receiver 104 demodulates transmit signal 110 to recover replicas ofhost signal 106 and overlay signal 108 from the transmit signal. Thephase rotation watermarking exploits an inherent phase trajectoryrotation between antipodal symbols of the host waveform (signal 106),e.g., BPSK, QPSK, or MPSK symbols, to carry the additional/overlay data(signal 108). When the host waveform transitions between adjacentsymbols which are antipodal (i.e., 180 degrees apart), there are tworotation directions the phase trajectory at the transition can take,either clockwise or counter-clockwise. Phase rotation watermarking usesthese two rotation direction possibilities to carry the additional data.In other words, the additional data modulates the direction of phaserotation, as will be described below.

Continuous Phase Modulation

Embodiments presented herein apply continuous phase modulation (CPM) tothe host waveform (signal 106). The CPM replaces discontinuous phasetransitions of an antipodal (BPSK), QPSK or other M-ary signal by asmoothed continuous trajectory. Phase rotation watermarking (PRW)modulates underlying CPM of the host waveform (signal 106) in accordancewith symbol states of the additional data (signal 108) to superimposethe additional data on the host waveform. With respect to CPM, two phaseshift keying cases to consider are: binary antipodal schemes, e.g.,Binary Phase Shift Keying (BPSK); and M-ary PSK. With BPSK, if a singlehost waveform, e.g., a pseudo-noise (PN) code, is to be transmitted on asingle quadrature channel, then a binary form of MSK can be used totransmit the code. In this case, two phases that are 180° apart (i.e.,“antipodal” phase states) can be used to respectively represent thebinary signal states. When using continuous phase transitions betweensymbols (referred to above as the “host symbols”) of the host waveforminstead of instantaneous phase transitions, there are two equivalentphase trajectory options available to perform the 180° phase transitionbetween the two antipodal phases: proceed in the counter-clockwisedirection for a total phase change of 180° (a positive phase shiftramp); or proceed in the clockwise direction for a total phase change of−180° (a negative phase shift ramp).

These two options are illustrated in FIG. 2 for the case where thecurrent symbol of the host waveform is a logical ‘1’ at a phase of 0°and the next symbol is a logical ‘0’ at a phase of 180°. Note that aninstantaneous phase change would proceed directly back and forth alongthe I-axis in the example shown in FIG. 2 (i.e., there is no rotationalpolarity); thus, the issue of phase rotation polarity exists in thecontext of phase modulated signals that employ continuous phasetransitions between adjacent symbols. Either rotational polarity willresult in the same end phases and both are identical in terms of the PNcode and the CPM.

A CPM BPSK phase trajectory with a fixed, positive phase transitionrotational is illustrated in FIG. 3. In this case, the symbol vectorproceeds with a counter-clockwise phase rotation around the unit circlefor all phase transitions, i.e., from a logical ‘1’ at 0° to a logical‘0’ at 180° and from a logical ‘0’ at 180° to a logical ‘1’ at 0°.

Alternating phase transition rotational polarity per transition is shownin FIG. 4. In this case, the symbol vector rotates back and forth from alogical ‘1’ at 0° to a logical ‘0’ at 180°. That is, a counter-clockwise(positive) phase rotation is used to transition from the ‘1’ phase stateto the ‘0’ phase state, while a clockwise (negative) phase rotation isused to transition from the ‘0’ phase state to the ‘1’ phase state. Notethat in this scheme, the phase trajectory always stays in the upper halfplane (as illustrated) or, alternatively, in the lower half plane if theopposite polarity convention is used (not shown). The quadrature (Q)component of the signal will therefore always be either positive (asshown in FIG. 3) or negative (in the convention not shown) for all phasetransitions. This introduces a DC bias and causes spurs to appear in thespectrum.

Where there is PN data on both the in-phase (I) and quadrature (Q)channels, such as with quadrature PSK (QPSK) or M-ary phaseconstellations, CPM can also be used to maintain a constant envelope.However, the possibility of +180° or −180° phase transitions betweenadjacent symbols still exists. As described earlier, host symbol phaseshifts of +90 or −90 can also be made to follow −270 or +270 phasetransition trajectories to carry the overlay symbol phase slopepolarity.

Phase Rotation Watermarking

As described above, CPM of the BPSK host waveform (signal 106) imposescontinuous phase transitions between adjacent symbols of the hostwaveform having antipodal phase transitions. In other words, the CPMimposes continuous, antipodal phase transitions on the BPSK hostwaveform. Phase rotation watermarking controls the direction of phaserotation (i.e., phase rotation polarity) of the continuous, antipodalphase transitions in accordance with/based on symbol state values of theoverlay symbols of the additional data, so that the direction of phaserotation of the continuous, antipodal phase transitions represents theoverlay/additional data. That is, the overlay/additional datawatermarks/modulates the direction of rotation of the continuous,antipodal phase transitions and, in this way, superimposes theoverlay/additional data on the host waveform. Similarly, as describedearlier for QPSK and by extension to any other M>=4 CPM waveform, theadjacent host symbol shifts can be encoded to yield the desired totalpolarity and slope of the phase transition rotation of each overlaysymbol as an average over all the host symbol phase transitions.

With reference to FIG. 5, there is shown a timing diagram of host signal106 (the host waveform) and overlay signal 108 (the additional data) inan example in which phase rotation watermarking uses the overlay signalto control the direction of the phase rotation of the transitions of theCPM host signal. In the example of FIG. 5, signal 106 is a high symbolrate signal and overlay signal 108 is a low symbol rate signal 106includes a sequence of host symbols having respective host symbols statevalues ‘1’ and ‘0’. In signal 106, transitions between ‘1’ and ‘0’, andvice versa, trigger continuous, adjacent antipodal phase transitions ofthe CPM, as described above. Overlay signal 108 includes a sequence ofoverlay symbols, i.e., symbols 502 and 504, having respective overlaysymbol state values of ‘1’ and “0.” Overlay symbols 502 and 504 eachhave an overlay symbol time or time interval T that spans multiple, R,host symbols of host signal 106. Each overlay symbol time interval T mayspan a set of any number of host symbols, such as 8, 12, 30, 62, 128,250, and so on host symbols.

Phase rotation watermarking assigns/maps a respective phase rotationpolarity (e.g., clockwise or counter-clockwise direction of rotation) toeach possible overlay symbol state/value (e.g., ‘0’ or ‘1’) that a givenoverlay symbol (e.g., symbol 502 or 504) of overlay signal 108 can takeon. Then, for each set of R host symbols, the phase rotationwatermarking imposes a common/same phase rotation polarity (e.g.,clockwise phase rotation or counter-clockwise phase rotation) on all ofthe continuous, antipodal phase transitions in the set of R host symbolsaccording to the overlay symbol state of the overlay symbol spanning theset of R host symbols. That is, phase rotation watermarking rotates allof the continuous, antipodal phase transitions in the set of R hostsymbols in a same direction according to the overlay symbol statespanning the set of R host symbols. As a result, in terms of phasechange, the phase rotation watermarking accumulates all of theindividual rotational phase changes in the same direction across eachset of R host symbols into a total phase change indicative of theoverlay symbol state of the overlay symbol spanning the R host symbols.This is akin to summing a series of small phase change ramps across theR host symbols into one big phase change ramp representative of theoverlay symbol state/value of the overlay symbol spanning the R hostsymbols. The total phase change across the big phase change ramp will benegative or positive depending on whether the common phase rotationpolarity is clockwise or counter-clockwise, respectively.

In the example of FIG. 5, the phase rotation watermarking assignsclockwise and counter-clockwise phase rotation polarities to overlaysymbol states/values ‘0’ and ‘1’, respectively. Thus, as shown in FIG.5, the phase rotation watermarking rotates all of the continuous,antipodal phase transitions 510 in the left-most R host symbols of hostsignal 106 in the counter-clockwise direction, according to the overlaysymbol state ‘1’ of overlay symbol 502 spanning those R host symbols. Asa result, the phase rotation watermarking accumulates a total positiverotational phase change over overlay symbol 502 that is representativeof the overlay symbol state ‘1’. In contrast, the phase rotationwatermarking rotates all of the continuous, antipodal phase transitions512 in the right-most R host symbols of host signal 106 in the clockwisedirection, according to the overlay symbol state ‘0’ of overlay symbol504 spanning those R host symbols. As a result, the phase rotationwatermarking accumulates a total negative rotational phase change overoverlay symbol 504, which is representative of the overlay symbol state‘0.’ To avoid wraparound of accumulated phase, techniques herein avoidsetting+/−N*2*PI values of accumulated phase equal to 0.

Phase Trajectory with Greater Degrees of Freedom in Waveform Design

As described above, the discontinuous phase transitions of the antipodal(BPSK), QPSK or other M-ary modulation signal of the host waveform (hostsignal 106) are replaced by a smoothed continuous trajectory. Thisenables a system designer to choose the most optimal phase trajectoryfunction and phase polarity pattern to fit the particular applicationrequirements for correlation loss and spectral content, as describedbelow.

One possibility is to obtain the phase as the integral of Gaussianfiltered frequency pulses of width T_(p), where the overall symbol timeof each host symbol of the host waveform is T_(s), and the ratio(T_(p)/T_(s)) and the Gaussian filter bandwidth is B form two parametersof the phase trajectory optimization space.

There many other possible phase trajectory functions that can be usedwith the phase rotation pattern aspect of this invention, each withtheir own unique spectral and correlation parameters. These can be theintegral of filtered frequency pulses where the filter transfer functionH(ƒ) is non-Gaussian. For example, a linear, a raised cosine, Bessel,Butterworth, Chebyshev, elliptical, arbitrary digital FIR, or IIRfilters could be used to filter the frequency pulses.

There are other arbitrary trajectory functions that are not evenexpressed in terms of an integral of a filtered frequency pulse, butrather by defining the continuous phase trajectory directly. There are alarge number of possible trajectory functions, but an optimal trajectorycan be found using the methodology described below.

The phase trajectory can be tailored to the particular transmissionchannel over which the system operates. Modern waveform generators usedigital signal processing methods, where N samples are used to representeach host symbol phase trajectory. Each sample is represented by a K-bitword, and there are 2^(NK) possible trajectories. Using common valuessuch as 8-bit words (K=8) and 6 samples per host symbol (N=6) revealsthat there is a large number of possible trajectories (2⁴⁸). However,the search space can be significantly narrowed using symmetryconstraints, because the trajectory function of the last three sampleswill be a mirror or inverted version of the first three samples. Thus,in this example, the search space is actually 2²⁴=1.7E+07 uniquetrajectory functions. This number is small enough that current computersimulation techniques can evaluate this number of possible trajectoriesin a reasonable amount of time and determine the optimal trajectory forthe application based on the spectral constraints and correlationrequirements. The actual number of possibilities can also be reduced byconstraining the phase trajectory to be monotonically increasing ordecreasing during each host symbol transition. Further, methods ofreducing the search space can be found and are beyond the scope of thisapplication. Once the optimal phase trajectory has been found, it can bestored in a look up table to be used in real time for the waveformgeneration using a digital signal processor (DSP) or field programmablegate array (FPGA).

First Example Transmitter Implementations

FIG. 6A is a block diagram illustrating the components of an exampletransmitter implementation of an RF modulation system 600 of transmitter102 capable of generating an antipodal (e.g., BPSK) transmit signalhaving a phase transition pattern of continuous, antipodal phasetransition trajectories resulting from phase rotation watermarking,which has the effect of superposing overlay signal 108 on host signal106. In this example, the underlying transmit signal (host signal 106)is a navigation signal having a PN symbol sequence; however, theinvention is not limited to navigation signals and is applicable toother suitable signal types.

Each of the various components shown in FIG. 6A essentially performscertain operations for generating the transmit signal, and individualcomponents can be implemented in hardware, software, or a combination ofhardware and software, as appropriate. For example, modulation system600 includes a processing capability generally represented by aprocessor 630, which can include, for example, one or moremicroprocessors, microcontrollers, or digital signal processors capableof executing program instructions (i.e., software) for carrying out atleast some of the various operations and tasks to be performed bymodulation system 600.

Modulation system 600 further includes one or more memory or storagedevices represented by memory module 640 to store a variety of data andsoftware instructions (control logic) for execution by processor 630.Memory 330 may comprise read only memory (ROM), random access memory(RAM), magnetic disk storage media devices, optical storage mediadevices, solid-state memory devices, flash memory devices, electrical,optical, or other physical/tangible (e.g., non-transitory) memorystorage devices. Thus, in general, memory 640 comprises one or moretangible (non-transitory) processor-readable or computer-readablestorage media that stores or is encoded with instructions (e.g., controllogic/software) that, when executed by processor 630, cause processor630 to perform the operations described herein. Memory 640 may alsostore various other data and information necessary for operation ofmodulation system 600.

While processor 630 and memory 640 suggest a processing environmentcomprising a data or signal processor that executes software stored in amemory, one or more of the components of modulation system 600 shown inFIG. 6A can be implemented in hardware as a fixed data or signalprocessing element, such as an application specific integrated circuit(ASIC) that is configured, through fixed hardware logic, to performcertain functions. Yet another possible processing environment is oneinvolving one or more field programmable logic devices (e.g., FPGAs), ora combination of fixed processing elements and programmable logicdevices.

Referring again to FIG. 6A, a phase mapper 602 phase maps an input(host) symbol sequence of host signal 106, e.g., an input navigationsymbol sequence, by assigning specific phases to the logical zeros andones of the input sequence. For example, each logical ‘1’ in the hostsymbol sequence can be mapped to the phase π/2 radians (90°), while eachlogical ‘0’ can be mapped to the phase −π/2 radians (−90°). Thephase-mapped PN/host symbol sequence is digitally sampled at a rate of Nsamples per symbol by a digital sampler 604, resulting in an outputsequence of phases ϕ(n). A phase differentiator 606 differentiates thesamples by comparing successive samples (ϕ(n)−ϕ(n−1)) to detect sampleswhere phase transitions occur. Phase differentiator 606 provides itsoutput to a multiplier 607. The output of phase differentiator 606 is amagnitude indicating the size of the phase step. This output generates apositive, pulse-like signal at the symbol boundary between host symbolsof different values (i.e., when a ‘0’ is followed by a ‘1’ or viceversa). For a phase transition in a BPSK signal, the phase step is ±π.The magnitude of the phase step in this example is π and is unsigned.

Concurrent with the operations performed by modules 602, 604, and 606,multiplier 607 receives overlay signal 108 including a sequence ofoverlay symbols representing logic levels ‘1’ and ‘0’ as overlay symbolstates/levels +1 and −1, respectively. In an embodiment, a symbol statemapper (not shown) may be used to map each logic level 1 or 0 of theoverlay signal 108 to the corresponding overlay symbol state +1 or −1.Each overlay symbol has a time interval T_b_wm that spans acorresponding set of R host symbols of host signal 106 in time. Eachoverlay symbol may also be referred to as a “phase rotation polaritysignal.”

Next, multiplier 607 multiplies the phase transition steps generated bythe magnitude of the differentiator 606 by the by the overlay symbolstates (+1 or −1) of signal 108, to patternize/modulate/impose thedirection of phase rotation from one antipodal host symbol to anotheraround the unit circle in accordance with the (mapped) overlay symbolstates. That is, the overlay symbol states rotate the continuous,antipodal phase transitions of the host waveform spanned by the symbolstates according to values of the overlay symbol states. Thus,multiplier 607 is more generally referred to as a “phase rotator.” Thesequence of overlay symbol states or phase rotation polarity signals ofsignal 108 represents a “phase transition polarity pattern” thatfollows/matches the sequence of overlay symbols states (whetherrepresented as logic levels ‘0’ and ‘1’ or as corresponding polaritysignals +1 and −1) of signal 108. This phase transition polarity patterncan represent a predetermined fixed sequence representative of awatermark sequence, an indeterminate sequence from some data source,random, or pseudo-random, and various sequence parameters can be chosento achieve desired spectral and correlation properties. As previouslydescribed, each phase rotation polarity signal (overlay symbol state) inthe pattern sequence (the sequence of overlay symbol states of signal108) is applied to the sampled PN signal over a span of R overlaysymbols since the output of symbol state mapper is constant over an Roverlay symbol interval. Multiplying the phase transition stepsgenerated by the magnitude of the differentiator 606 by the phaserotation polarity signal preserves the time of the transitions withinthe PN sequence but sets the transition polarity based on the pattern.

Referring once again to FIG. 6A, an FIR filter 610 having L taps, whereL is less than or equal to the total number of samples N in a hostsymbol, can be used to repeat the phase transition samples L times suchthat, for each phase transition, the first L out of the total of Nsamples in the host symbol are used for the phase transition trajectory.By way of a non-limiting example, each of the L taps of FIR filter 610can have a coefficient=1. According to another approach, FIR filter 610can have N taps and have the first L coefficients=1, while the remainingL-N coefficients are set to zero. The purpose of the FIR filter is tocontrol the fraction of the host symbol (L/N) during which the phase isin transition. For example, if there are 12 samples per host symbol(N=12) and L=6, then during the first half of the host symbol the phasecan be transitioning while during the second half (the last 6 samples),the phase is relatively constant. Note that conventional MSK (linearramp phase transition) and GMSK (Gaussian phase transition) CPMtechniques have the phase transition occurring over the entire hostsymbol interval (i.e., L=N). In the above described technique, theportion of the host symbol interval over which the phase transitionoccurs can be controlled by setting the value of L to less than or equalto N. The number of non-zero-coefficient taps L (and consequently theratio L/N) and the Gaussian filter bandwidth B both affect the resultingspectrum and correlation function of the output signal and can be chosento achieve the desired spectral and correlation properties for aparticular application. If L is a relatively small number (e.g., closerto 0 than N), then the phase transition between adjacent host symbols isrelatively short and the resulting modulation tends to have correlationand spectral properties more like that of a signal with instantaneousphase transitions. If L is a relative large number (e.g., closer to Nthan 0), then the phase transition between adjacent host symbols isrelatively long, and the spectral characteristic of the signal are morelike that of a typical CPM signal (though the correlation function,while suffering some correlation loss, may nevertheless maintain deepnulls like the instantaneous phase transition signal due to the phaserotation polarity pattern described herein). Generally, since the hostsymbols each comprise the plurality of N samples, and the phasetrajectory of the continuous phase transitions extends over L samples, Lmay be less than or equal to N. Thus, in one embodiment, the phasetrajectory of the continuous, antipodal phase transitions extends overan entire host symbol. In another embodiment, the phase trajectory ofthe continuous, antipodal phase transitions extends over only part of ahost symbol.

For each phase transition, the output of FIR filter 610 is essentially aset of L time-domain samples. A Gaussian digital filter 612 for shapingthe frequency samples applies a transfer function h(n) to the L repeatedsamples to produce an instantaneous frequency output signal ƒ(n). By wayof a non-limiting example, the Gaussian filter can apply the followingtransfer function:

${h(n)} = {\sqrt{\frac{2\pi}{\ln\; 2}}{Be}^{(\frac{{- 2}\pi^{2}{B^{2}{({nT}_{s})}}^{2}}{\ln\mspace{11mu} 2})}}$where B is the bandwidth of the filter. The filter bandwidth B can bechosen to provide the desired output spectrum and correlationperformance. However, a Gaussian filter may not be the optimal filterfor a given application, and another low pass filter that suitablyshapes the frequency samples can be used. Furthermore, a suitable filtertransfer function can be used to compensate for the nonlinear RF poweramplifier characteristics and characteristics of downstream filters. Thefrequency pulse shape can be optimized to comply with the transmitterspectral requirements while providing the lowest correlation loss anddeepest nulls in the cross-correlation function in the user receiverfront-end bandwidth, and/or highest possible RF signal level in thereceiver bandwidth. The output of Gaussian filter 612 is essentially asequence of L time-domain samples, smoothed in accordance with theGaussian filter response, which serve as an instantaneous frequencysignal ƒ(n) that, when integrated, forms the desired phase transitiontrajectory.

The instantaneous frequency signal ƒ(n) is supplied to a phaseintegrator 614 that integrates the frequency signal according to:

${\varphi(n)} = {\varphi_{i} + {\sum\limits_{k = 0}^{n}{f(k)}}}$

where φ_(i) is the initial phase, to produce a cumulative phasetrajectory signal φ(n) that provides a smooth phase step betweenadjacent host symbols having different values.

The cumulative phase trajectory signal φ(n) is supplied to a constantamplitude polar-to-rectangular converter 616, which computes theconstant envelope I(n) and Q(n) waveforms as the cosine and sine of thephase trajectory signal and passes them as inputs to a quadraturemodulator 618. Quadrature modulator 618 is supplied with the transmitcarrier frequency via a local oscillator 620 and generates as its outputthe desired continuous phase RF signal for transmission. The RF signalrepresents a phase modulated signal including (i) a sequence of hostsymbols having continuous, antipodal phase transitions between adjacenthost symbols representing different states, and (ii) a sequence ofoverlay symbols each spanning a respective set of the host symbols intime, wherein the continuous, antipodal phase transitions in each set ofthe host symbols are rotated in a same rotation direction according to asymbol state of the respective overlay symbol spanning the set of hostsymbols.

As will be appreciated from the foregoing description, a variety ofimplementations are possible by selecting certain parameters such as:the number L of samples per host symbol used to perform the phasetransition; the shape of the phase trajectory (e.g., Gaussian, linear,etc.); and the phase rotation polarity pattern. For example, a full MSKversion of the waveform can be generated by using all of the samples ina host symbol (L=N), without filtering and integrating to yield a linearphase transition, whereby the phase is linearly ramped during the entiresymbol interval. According to another example, a partial MSK version ofthe waveform can be generated by using only a fraction of the samples ina symbol (L<N) for a linear phase transition, with the phase beingconstant for the remainder of the host symbol. According to yet anotherexample, a full GMSK version of the waveform can be generated by usingall of the samples of a symbol (L=N), wherein the phase follows anintegrated-Gaussian trajectory during the entire host symbol interval. Apartial GMSK version can be achieved by using only a fraction of thesamples in a symbol (L<N) for the phase transition, with the phase beingconstant over the remaining portion of the host symbol. Phasetrajectories other than linear and Gaussian can also be used.

FIG. 6B is a block diagram illustrating an example transmitterimplementation of an RF modulation system 650 similar to system 600,except for the addition of a phase rotation polarity pattern generator608 and a second multiplier 652 to modulation system 650. Phase rotationpolarity pattern generator 608 randomizes or patternizes the directionof phase rotation described above from one antipodal symbol to anotheraround the unit circle. Such randomization or patternization of therotational polarity achieves both desirable spectral qualities andcorrelation qualities.

Pattern generator 608 generates a phase rotation polarity signal havinga sequence of values of +1 or −1 in accordance with a phase transitionpolarity pattern being deployed. Each symbol in the polarity signaloutput by pattern generator 608 has a symbol or bit time T_b_pg, whereT_b_pg=M* host symbol time (M is an integer). The phase transitionpolarity pattern can be a random, pseudo-random, or predetermined fixedsequence, and the sequence parameters can be chosen to achieve desiredspectral and correlation properties. The output sequence of patterngenerator 608 is multiplied by the sequence of overlay symbols ofoverlay signal 108 (the additional data) by multiplier 652, and theresulting product is provided to multiplier 607. Multiplier 607multiplies the phase transition steps generated by the magnitude of thedifferentiator 606 by the product output by multiplier 652. Aspreviously described, each phase rotation polarity signal in the patternsequence from multiplier 652 is applied to the sampled PN signal over aspan of R symbols.

In one embodiment, the overlay symbol/bit time T_b_wm for signal 108 isin general much longer than the symbol/time T_b_pg for the patterngenerator 608, i.e., T_b_wm>>T_b_pg. In a case where there are longerperiodic characteristics included in the phase rotation polarity patternof pattern generator 608 for desired spectral and correlationproperties, the additional data bit time must also be longer that thetime constants associated with those characteristics. This ensures thatthe spectral and correlation properties of the phase rotation polaritypattern from pattern generator 608 will not be altered due to theadditional data (of overlay signal 108). In another embodiment, there isno constraint on the relationship between the bit times T_b_wm andT_b_pg. For example, the bit times may be equal in order to ensure thatthe phase rotation of the (phase transition) modulation is random evenif the additional data (signal 108) is not (e.g., long sequences of “1s”and “0s”), in order to ensure that the correlation and spectralproperties will be preserved.

FIG. 7A is a time-domain graph illustrating the output phase trajectoryφ(n) of an example phase integrator over a span of 60 samples (five hostsymbols). In this example, the shape of the phase trajectory reflects aGaussian filter, because a Gaussian CPM BOC(10,5) is used, where BT=1.2and L=5. In this example, the number of samples per host symbol (N) is12, such that L/N= 5/12. This means that the input frequency pulse tothe Gaussian filter is 5/12^(ths) of the host symbol in duration. Theoutput of the Gaussian filter is integrated to obtain the phasetrajectory shown. Other filters would produce a different phasetrajectory. Note that each overlay symbol state (+1 for ‘1’ or −1 for‘0’) is constant over each R overlay symbol interval (i.e., within anygiven R overlay symbol interval, the phase transitions are either allpositive or all negative). In the example shown in FIG. 7A, because thenumber of overlay symbols depicted is far fewer than R, all of the phaserotation transitions have the same polarity in this interval, in thiscase, a positive phase ramp.

FIG. 7B is a time-domain graph of the same output signal shown in FIG.7A (a Gaussian CPM Binary Offset Carrier (BOC)(10,5), BT=1.2, L=5, N=12)but “zoomed out” to show a sequence of 6 overlay symbol state intervalsin the phase rotation polarity pattern imposed on/applied to the hostwaveform, in this case spanning 9216 samples (note that FIG. 7A shows amuch smaller span of 60 samples). From the left side of the graph, thephase rotation polarity is positive (+1) over the first R host symbolinterval (a set of 128 host symbols) corresponding to one overlay symbolstate (spanning the set of 128 host symbols), followed by an second Rhost symbol interval in which the phase rotation polarity is negative(−1) corresponding to a next overlay symbol state. In this example,R=128. The third and fourth R host symbol intervals have a positive (+1)phase rotation polarity corresponding to two more overlay symbol states,followed by fifth and sixth R host symbol intervals in which the phaserotation polarity is again negative (−1) corresponding to a next overlaysymbol state. Thus, in this example, the phase rotation polarity patternsequence shown is: +, −, +, +, −, −, representing an overlay symbol(state) sequence of 101100. That is, the sequence of overlay symbolstates 101100 has been applied to the phase rotation, so that each 128host symbols comprises one symbol of the superimposed additional data.

Considering, for example, the first R overlay symbol interval shown,while the graph appears to be a substantially straight line extendingfrom 0 to about 360 radians over about 1500 samples, in fact, if onewere to “zoom in” to look at a segment of this “line” it would actuallylook like the curve shown in FIG. 7A, reflecting the Gaussian phasetrajectory.

FIG. 7C is a signal vector scatterplot diagram for the same waveformshown in FIGS. 7A and 7B (a Gaussian CPM BOC(10,5), BT=1.2, L=5, N=12).In this example, the two antipodal phase states are located at 45° and225°. The scatterplot shows groupings of phase states dwelling aroundthe two antipodal phase states and six sample phase transitions betweenthe two phase states, which essentially trace out the Gaussian phasetrajectory.

FIG. 7D is a frequency-domain graph of the power spectrum of thewaveform of FIGS. 7A-7C compared with a reference binary phase shiftkeying (BPSK) BOC(10,5) waveform with instantaneous phase transitions.Note that power spectrum of the waveform has significantly lowersidelobes (i.e., faster rolloff of sidelobes) than the reference BPSKwaveform, similar to a conventional CPM waveform such as GMSK, sincesmoother phase transitions reduce the higher frequency components of thewaveform. However, unlike conventional CPM waveforms, which transitionthe phase continuously over the entire symbol period, the schemedescribed herein allows the designer to control the shape and rolloff ofthe sidelobes by choosing the values of L (the number of samples overwhich the phase transition occurs) and B.

FIG. 7E is a graph illustrating the cross correlation of the waveform ofFIGS. 7A-7D compared to the reference BPSK BOC(10,5) waveform. Notably,the steep nulls are preserved in the Gaussian CPM BOC(10,5) waveform asa result of the phase rotation polarity pattern of the phase transitionsbeing uncorrelated with the PN code of the signal. The preservation ofthe deep nulls in the cross correlation is a significant differencebetween this waveform and a conventional CPM waveform (see FIG. 4A)owing to the phase rotation polarity pattern being uncorrelated with thesymbol sequence (e.g., the PN code of the transmit signal). The peak ofthe cross-correlation curve of the Gaussian CPM BOC(10,5) waveform issomewhat lower than that of the reference BPSK waveform as a result ofcorrelation loss owing to the continuous phase transitions.

FIG. 7F is a frequency domain graph illustrating the output spectrum ofa saturated high power RF amplifier using the waveform of FIGS. 7A-7E(Gaussian CPM BOC(10,5)) compared with the reference BPSK BOC(10,5).Note that the reduced spectrum is preserved in the constant envelopesignal at the output of the non-linear RF amplifier. This result showsthat a bandwidth efficient waveform has been achieved at the output ofthe power amplifier.

Extension to M-Ary Modulation

While the foregoing description focuses on antipodal modulation schemesin which the two possible phase states are 180° out of phase, thedescribed techniques can be extended to phase modulation schemesinvolving M-ary phase constellations. This context is important becausemultiple navigational codes can be combined on I and Q channels to forma composite waveform having M possible phases. Some examples of M-aryconstellation transmission of time acquisition codes are:

1. Sending one code on each quadrature;

2. Using majority vote to combine two or more codes on each quadrature;

3. Interplex combining; and

4. POCET combining.

The described system is extended to these M-ary waveform cases toprovide a reduced spectral occupancy and desired correlationperformance. More specifically, when there is a phase transition in aCPM waveform, the signal vector transitions between the M phases of theconstellation by moving along the unit circle to provide a constantenvelope waveform. As previously described, a fraction (L/N) of thesamples of a host symbol, where L≤N, can be used to effect the phasetransition between adjacent host symbols. The phase trajectory functioncan be linear, integrated Gaussian, or other smoothed function, as inthe antipodal case, to provide desired spectral and correlationproperties. Even with an M-ary constellation, there are instances wherethe phase transition between adjacent host symbols requires a 180° phasetransition. For example, suppose a QPSK waveform uses a constellation offour phases at 45°, 135°, 225°, and 315° to represent the logical values00, 01, 11, 10, respectively. In this case, if adjacent host symbolsrepresent the values 00 and 11 or if adjacent host symbols represent thevalues 10 and 01, a 180° phase transition is required. According to thedescribed system, in an M-ary waveform, when the phase transitionbetween two adjacent host symbols is 180°, the previously describedphase rotation polarity pattern can be employed to determine thedirection of the 180° phase transition, as in the antipodal case. Whenthe phase transition between the QPSK host symbols is +90 or −90degrees, then there are several embodiments. One embodiment may chooseto use only the antipodal phase state shifts of the host waveform forencoding the overlay waveform. An alternative embodiment may also encodethe +90 and −90 degree transitions of the QPSK host waveform asdescribed previously using possibilities of +90, −270 and −90, +270 suchthat the average phase shift over the overlay symbol has the desiredphase shift polarity and slope value to be demodulated by the overlayreceiver processing (e.g., Differential PSK or BFSK).

The example transmitter implementations shown in FIGS. 6A and 6B in thecontext of an antipodal waveform can be extended to M-ary modulation asfollows. After mapping the input sequence to the M-ary phaseconstellation and sampling the signal at N samples per host symbol, thephase transition position, polarity, and magnitude of each phasetransition are found by differentiating the samples. Note that themagnitude of the phase transitions must be determined to be able todifferentiate between phase transitions of 180° and smaller phasetransitions. Phase transitions that are determined to be less than 180°are passed to the FIR filter 610 unchanged (i.e., no phase rotationpolarity modification is made). For phase transitions that are 180°, theoutput of the symbol state mapper are applied to the output of thedifferentiator 606 as previously described to modify the phase rotationpolarity to superimpose the overlay symbol states of overlay signal 108on the phase modulation of host signal 106. The remaining processing isthe same as previously described in the antipodal case.

In a second implementation of M-ary modulation, even the non-antipodalphase transitions can be transmitted to carry the overlay data as wasdescribed above in the QPSK case. For each phase shift the modulator canchoose to get there via the shortest trajectory around the unity circleshown in FIG. 2, or it can get there using the long way around. For eachoverlay symbol that is being sent, the modulator chooses the phasetrajectory of each of the host symbol transitions in such a way that thesum total phase transitions over the host symbols corresponds to thedesired target phase step corresponding to the transmitted overlaysymbol.

Thus, phase rotation watermarking may be applied to M>=4 modulations onall symbol phase transitions, both antipodal (phase shift=180 degrees)and non-antipodal. For example with Q-ary CPM, the watermarking may beapplied to phase shifts of +90, 180, or −90 degrees as follows. Thewatermarking method for the case of a 180 degree phase shift has alreadybeen described. For a symbol phase shift of 90 degrees, the phasetransition may be either +90 degrees in the CCW direction, or −270degrees in the CW direction. This is depicted in FIG. 4B, which is anillustration of a host Q-ary CPM constellation showing two possiblephase transitions for a 90 degree host symbol shift, allowingwatermarking to be applied for non-antipodal adjacent symbol states.Similarly, for a symbol phase shift of −90 degrees, the phase transitionmay be either +270 degrees in the CCW direction, or −90 degrees in theCW direction. These possibilities may be averaged over an overlay symbolof multiple host symbols to arrive at a desired average phase shiftslope for the overlay symbol. For example, if the overlay symbol is tobe encoded as a positive phase shift slope, and the host signal is aQPSK waveform, then each time the host symbol shift is 90 degrees or −90degrees, then the total number of host phase transitions that are equalto +90, −90, +270 or −270 would be chosen such that the average of allthe host phase transitions over the overlay symbol interval would beeither +180 or −180 as in the case where the host is a BPSK CPMwaveform. In summary, for the M>=4 case, both the antipodal and thenon-antipodal continuous phase transitions of the host waveform are usedto carry the data of the overlay symbols. The non-antipodal host phasetransitions are controlled by the modulator and encoded to either takethe long or short way around the unit circle (i.e., a longest phase pathor a shortest phase path) while transitioning to the adjacent phasestate, such that the average direction and speed of the phase rotation,or the cumulative phase shift, over the duration of the overlay symbolsis encoded to carry the data of the overlay symbols.

Phase rotation watermarking does not require constant amplitudemodulation and is therefore not limited to the constant phase modulationtechniques described above. Phase rotation watermarking may be appliedto Quadrature Amplitude Modulation (QAM) as well. In that case, whenevera 180 degree phase transition takes place in the host waveform (hostsignal 106), the modulation follows either the CW or CCW direction tocarry the overlay signal or “watermark” information. The end symbolswould be the same as described above, and only the transition would beused to carry the watermark. Even in this case the watermark would nothave to have a significant impact on the host waveform performance. Forexample, in 16 QAM, each symbol has a 1 in 16 (0.0625) chance oftransitioning to a symbol 180 degrees away. The RF waveform thereforehas two possible rotation trajectories which are identical for theregular user. These two possibilities can be used for phase rotationwatermarking. Even though the amplitude is varying, and only one in 16symbols would carry the phase rotation watermarking information (overlaysymbol states), over time a detector looking for the watermark (overlaysymbol states) would accumulate enough phase shift to demodulate thewatermark, albeit at a much lower data rate than the host waveform. Inthis example, for every 1000 symbols of the host waveform, there wouldbe an average of 62 host symbols that could carry watermark (overlaysymbol) information. Or, adjacent symbol state shifts which are withinsome distance of +180 or −180 can still be rotated in either directionas needed to carry the phase slope of the overlay symbol. The modulatorcan control the transitions of each of the host QAM symbols of theoverlay symbol over the I-Q space so as to effect a total phase shiftequal to the desired phase shift of the overlay symbol.

Second Example Transmitter Implementation

FIG. 8 is a block diagram illustrating components of another exampletransmitter implementation of a modulator system 800 capable ofgenerating an antipodal (e.g., BPSK) transmit signal having continuousphase transition trajectories according to phase rotation watermarkingwherein the phase rotation polarity pattern follows the sequence ofoverlay symbol states of overlay signal 108. Compared to the firstexample transmitter implementations shown in FIGS. 6A and 6B, theimplementation shown in FIG. 8 relies more heavily on hardware thandigital signal processing to apply the phase rotation polarity patternand to produce the transmit signal.

In the example shown in FIG. 8, a waveform generator 802 generates adigital baseband time-domain sample stream representing a BPSK BOC(10,5)waveform (signal 106), which is split and supplied both to an I-channel(I(t)) and to a Q-channel (Q(t)). The sample stream I(t) is supplied toan I-channel delay device 804 (“delay X samples”), and the sample streamQ(t) is supplied to a Q-channel delay device 806 (“delay Y samples”). AnX, Y Samples Delay Controller 808 controls delay devices 804 and 806 toselectively delay either the I(t) or Q(t) signal by L samples. Thedecision of whether the I(t) or Q(t) signal is delayed is determined bythe output of the delay controller 808. The selection of delaying I(t)or Q(t) is equivalent to selecting a positive or negative phase rotationat the downstream hard limiter output. Thus, in this implementation, thedelay controller 808 essentially operates as the symbol state mapper byselectively applying delays to the I and Q channel signals to create aphase rotation polarity pattern representative of the sequence ofoverlay symbol states of signal 108. In effect, this implementationprovides a different way of generating a CPM waveform while“patternizing” the polarity of the 180° phase transitions in accordancewith overlay signal 108.

After selective application of a delay to the signals I(t) and Q(t), theresulting I and Q signals are then filtered by respective low passfilters 810 and 812 to produce filtered baseband I and Q signals, andthen supplied to a quadrature phase shift keying (QPSK) modulator 814.QPSK modulator 814 includes an I-channel mixer 816 that mixes thefiltered baseband I signal with a carrier frequency signal supplied by alocal oscillator 820, which has been phase shifted by −90° relative tothe Q-channel by a phase shifter 822, to produce a carrier-frequencyI-channel signal. QPSK modulator 814 further includes a Q-channel mixer818 that mixes the filtered baseband Q signal with the carrier frequencysignal supplied by local oscillator 820 to produce a carrier-frequencyQ-channel signal.

A combiner 824 combines the carrier frequency I-channel and Q-channelsignals, and the output of combiner 824 is hard limited by a hardlimiter 826 (e.g., a saturated amplifier) at low power. Alternatively,the carrier frequency I and Q signals can be hard limited in DSPprocessing by first converting the I and Q signals from rectangular topolar format, then fixing the amplitude to be constant, and thenconverting back to a rectangular (I and Q) format. The resultingconstant envelope waveform preserves the phase information of the signaland can be fed as the input to a saturated amplifier such as atravelling wave tube or a solid state amplifier. Because the waveformhas a constant envelope, the spectral regrowth through the saturatedamplifier is minimized.

The parameters of the low pass filters 810 and 812 can be optimized toprovide the best bandwidth efficiency and correlation performancetradeoff. These include the filter characteristic function andbandwidth. By way of non-limiting examples, analog, digital FIR, ordigital IIR filters can be used.

As with the first example implementation, the second exampleimplementation can be extended to apply to M-ary modulation schemes. Inparticular, the waveform generator 802 of FIG. 8 generates a basebandM-ary waveform and, when a phase transition of 180° occurs, the sampledelay controller 808 delays either the I or Q signal by L samples inaccordance with the phase rotation polarity pattern, as previouslydescribed. For phase transitions less than 180°, sample delay controller808 does not apply any delay to the I and Q signals, and the processingotherwise remains essentially the same.

Example Receiver

With reference to FIG. 9, there is a block diagram of an example ofreceiver 104 to receive and process RF phase modulated transmit signal110 transmitted from transmitter 102. Receiver 104 includes an antenna902, an RF front-end 904, a host waveform receiver 906, and anadditional data receiver 908 that operates in parallel with the hostwaveform receiver. Antenna 902 captures signal 110 and delivers it to RFfront-end 904. RF front-end includes, in series: an RF filter 904 a tofilter the RF signal captured and delivered by the antenna; a low noiseamplifier (LNA) 904 b to amplify the filtered RF signal; afrequency-downconverter (FDC) or mixer 904 c to frequency down-convertthe amplified RF signal to produce frequency-downconverted quadrature Iand Q signals; and an analog-to-digital converter (ADC) to digitize theI and Q signals and provide them to the host waveform receiver 906 andadditional data receiver 908 in parallel. The frequency-downconverted Iand Q signals may be at baseband, or at an intermediate frequencybetween baseband and the RF frequency of signal 110.

In an embodiment, host waveform receiver 906 includes a host waveformdemodulator 910 to demodulate the phase modulated host symbols conveyedin signal 110, to recover and output a replica of signal 106 (i.e.,demodulated host waveform data). Demodulator 910 may include aGMSK/BPSK/DPSK or other type of demodulator to demodulate thecorresponding type of modulation used to modulate the host symbols ofsignal 106. In another embodiment, host waveform receiver 906alternatively, or additionally, includes a GPS/GNSS (i.e.,navigation-related) receiver 912, including: a correlator 912 a tocorrelate the host symbols against a local code; a detector to detectthe correlated signal; and an early/late (E/L) discriminator toascertain a best estimate of the time offset of the correlated signalused to calculate time and position. GPS/GNSS receiver 912 outputsGPS/GNSS time, position, and message data.

Additional data receiver 908 (also referred to as a “watermarkdemodulator” or an “additional data demodulator”) operates on the I andQ signals from RF front-end 904 in parallel with, but independent of,host waveform receiver 906. Additional data receiver 908 may use any ofseveral methods, including a binary frequency shift keying (BFSK)detection method and a DPSK detection method, to extract the additionaldata (i.e., overlay symbols of signal 108) from the I and Q signalsderived from signal 110.

The BFSK detection method is described first. In this method, additionaldata receiver 908 is configured as a BFSK demodulator. As describedabove and shown in FIG. 7B, phase rotation watermarking of continuous,antipodal phase transitions results in either a positive or a negativephase slope/ramp that accumulates over R symbols spanned by an overlaysymbol (state). The positive or negative phase slope is indicative ofthe overlay symbol state. The positive or negative phase slope isactually a positive shift in frequency or a negative shift in frequencyaway from a carrier frequency. That is, the phase slope, whendifferentiated, represents the frequency shift. Therefore, a now knownor hereafter developed BFSK demodulator may be used to detect thepositive and the negative frequency shifts corresponding to the positiveand negative slopes. The +/−frequency offsets may be calculated from theslope of the phase function (slope) over the time interval of theoverlay symbols, which are in general much longer than the timeintervals of the host symbol modulation waveform.

The DPSK detection method is now described. In this method, additionaldata receiver 908 is configured as a DPSK demodulator. The DPSKdemodulator calculates a phase corresponding to each I and Q sample pairfrom RF front-end 904. Then, the DPSK demodulator computes anincremental phase difference between each current and previous samplepair, and sums the incremental phase differences across/for all of thesample pairs over the time interval of the overlay symbol, to produce atotal phase shift over, and representative of, the overlay symbol (thisis performed repeatedly for each (modulated) overlay symbol in signal110). The polarity of this phase shift determines the demodulatedoverlay symbol state/data bit; a positive phase shift results in a DPSKdemodulator output of ‘1’ and negative phase shift results in an ofoutput of ‘0’.

With reference to FIG. 10, there is a block diagram of a DPSKdemodulator 1000 that may be used in additional data receiver 104 todemodulate phase rotation watermarking (i.e., the overlay symbols).Demodulator 1000 includes a phase detector 1002 to compute incrementalphase differences between successive pairs of I and Q samples from RFfront-end 104, a phase accumulator 1004 to accumulate the incrementalphase differences over a time interval of an overlay symbol, and asymbol state determiner 1006 that samples an output of the phaseaccumulator (which will have accumulated either a positive or a negativephase ramp) once per overlay symbol time interval to determine theoverlay symbol state (‘1’ or ‘0’) for that time interval. A timingsignal indicative of the overlay symbol time interval resets phaseaccumulator 1004 and triggers sampling of determiner 1006 once everyoverlay symbol time interval.

Both the BFSK and DPSK demodulators described above may be non-coherent.The host and overlay symbols could be used to derive symbol time thesame way any conventional BFSK and DPSK demodulators derive symbol time.For coherent detection of the additional data, a known preamble patternmay be sent at the start of each additional data “frame.” Thedemodulator may first correlate with the preamble to determine a phaseoffset, and then perform its demodulation coherently. This would resultin a performance improvement in an associated BER vs. E_(b)/N_(o) curve,compared to non-coherent detection.

In the embodiments or receiver 104 described above, host waveformreceiver 906 and additional data receiver 908 are parallel, independentreceivers. In another embodiment, receivers 906 and 908 may beintegrated, or their various functions may be integrated. For example,in a navigation system, overlay symbols of overlay signal 108 may bedetected first and then used for coarse acquisition of time/frequencyand phase for processing of host symbols of host signal 106. In thenavigation system, the overlay symbols of overlay signal 108 mayrepresent an overlay code, while the host symbols of host signal 106represent a “baseline” underlying code. Thus, receiver 104 acquires theoverlay code for coarse time and position, and then uses this totransition to the underlying code, which is at a higher bandwidth, forfiner more accurate time and position estimation. For example, in acurrent navigation system, receivers first acquire a C/A code and thenacquire a P waveform. This requires two separate codes to be transmittedand combined. With the method described herein, the coarse code can beembedded in the waveform of the fine code so that no additional codeneed be transmitted.

More specifically, phase rotation watermarking may be used as a coarsecode in GPS/GNSS for acquisition prior to transition to a fine highbandwidth code. That is, a GPS/GNSS navigation code similar to the C/Acode is transmitted by superimposing it on the finer higher bandwidthcode using the phase rotation watermarking. In a receiver, a localversion of the “watermarked” coarse code consisting of the rising andfalling phase ramps as shown in FIG. 7B is correlated with incoming Iand Q samples from RF front-end 904 and shifted in time until a peak isdetected. Similarly, the delta early and late versions used incorrelator 912 a are combined to form the early/late discriminatoroutput of 912 c as is done for the standard GPS/GNSS waveforms, as wellas demodulating navigational messages sent along with the coarse code,as is done when receiving the C/A code before transitioning to thehigher bandwidth codes. Acquisition of coarse time and position, anddemodulation of the navigational message would enable the receiver totransition to acquisition of the finer high bandwidth code in a moreefficient, resilient manner than trying to acquire the high bandwidthcode directly.

Similarly, this method can be used as a more efficient method ofcommunication links to embed coarse and fine acquisition codes into asingle transmitted waveform. Some receivers would acquire the coarsewaveform and demodulate the lower bandwidth data in the watermarkingoverlay and stop there, while others could use the coarse code as aprelude to acquiring the fine code and demodulate the high bandwidthdata. Still other receivers may only have the encryption key for eitherthe watermark data or the baseline code, and would not be able to seethe other layer of data.

Summary

In summary, phase rotation watermarking provides a simple, robust, hardto detect, method of using a host data stream to carry additional datawith minimal degradation to its performance. Phase rotation watermarkingexploits the inherent phase trajectory rotation ambiguity that existsbetween antipodal symbols of a BPSK, QPSK, MPSK, or other host waveformto carry an additional data channel. When the host waveform transitionsbetween its adjacent symbols which are antipodal (180 degrees apart)there are two equivalent directions the phase trajectory can take,either clockwise or counter-clockwise. Phase rotation watermarking usesthese two direction possibilities to carry additional information. In analternate implementation, for M>=4 PSK modulation, phase rotationwatermarking can even use the non-antipodal shifts in the host symbolsto carry the overlay data, by using both the shortest phase path (i.e.,short way) and the longest phase path (i.e., long way) around the unitcircle between adjacent phase states to achieve an average or cumulativepositive or negative phase rotation polarity during the duration of theoverlay symbol. Phase rotation watermarking requires less hardwarecomplexity than many of the other methods in use. For CPM systems,minimal changes are needed to the modulator hardware as the phaserotation is already being generated by the modulation.

Numerous communication systems currently using BPSK, QPSK, M-ary PSK,and QAM modulations and can be modified to use phase rotationwatermarking to send additional information across a transmissionchannel. Such applications include digital transmission of video, usingthe phase rotation watermarking overlay to carry audio and othermessaging simultaneously with the host waveform. Also, digitaltelevision standards currently in place for space, terrestrial, andcable transmission (DVB-T, DVB-S, DVB-C, DSS) all use modulations thatcan use phase rotation watermarking. In addition, Sirius XM satelliteradio uses QPSK transmission which can be overlaid with phase rotationwatermarking. Applications include covert messages sent over thesepublic transmission channel which can only be detected by phase rotationwatermark receivers, with appropriate encryption for privacy, or publicservice messages for all users. Also, digital storage of software,movies, music, photographs, and other documents, may use the phaserotation watermarking to overlay authentication to detect, prevent, anddiscourage unlawful distribution.

Civilian GPS receivers may recover a phase rotation watermarking overlaychannel to automatically receive updated map and services informationfrom any location in the world independent of cell phone or internetinfrastructure GPS receivers could receive region-specific publicservice announcements regarding emergency situations, independent ofnormal cell phone infrastructure. Military users could use their GPSreceivers to receive covert, encrypted, region specific, incoming datafrom any point on earth, independent of any other infrastructure.

Software Defined Radio (SDR) technology is fast becoming a popularapproach to design communication equipment. This technology allows thesame hardware to be configured in multiple ways depending on thesoftware/firmware installed. Phase rotation watermarking would allow SDRradios to receive automatic updates so that they could be reconfiguredin the field. Applications include automatic reconfiguring of TVreceivers (terrestrial, satellite, or cable), satellite radio receivers,and other user equipment by a central office. This could be used toupdate to a new transmission standard, to correct a software bug, or toprovide improved performance applicable to both civilian and MilitaryGPS users.

In summary, in one aspect, a method is provided comprising: generating asequence of phase modulated host symbols having continuous, antipodalphase transitions between adjacent ones of the host symbols representingdifferent states; receiving a sequence of overlay symbols each spanninga respective set of the host symbols; rotating the continuous, antipodalphase transitions between the adjacent ones of the host symbols in eachset of the host symbols in a same rotation direction according to asymbol state of the respective overlay symbol spanning the set of thehost symbols; and generating a phase modulated transmit signal thatconveys the continuous, antipodal phase transitions rotated according tothe symbol states of the overlay symbols.

In yet another aspect, an apparatus is provided comprising a basebandsignal generator to generate a sequence of phase modulated host symbolshaving continuous, antipodal phase transitions between adjacent ones ofthe host symbols representing different states; a phase rotator toreceive a sequence of overlay symbols each spanning a respective set ofthe host symbols, and to rotate the continuous, antipodal phasetransitions between the adjacent ones of the host symbols in each set ofthe host symbols in a same rotation direction according to a symbolstate of the respective overlay symbol spanning the set of the hostsymbols; and an RF modulator to generate a phase modulated transmitsignal that conveys the continuous, antipodal phase transitions of thephase modulated host symbols rotated according to the symbol states ofthe overlay symbols.

In another aspect, an apparatus is provided comprising: a radiofrequency (RF) front-end to receive an RF signal and frequencydown-convert the RF signal to a down-converted signal, wherein the RFsignal and the down-converted signal each conveys (i) a sequence ofphase modulated host symbols having continuous, antipodal phasetransitions between adjacent host symbols representing different states,and (ii) a sequence of overlay symbols each spanning a respective set ofthe host symbols in time, wherein the continuous, antipodal phasetransitions in each set of the host symbols are rotated in a samedirection according to an overlay symbol state of the respective overlaysymbol spanning the set of host symbols; a first demodulator todemodulate the host symbols from the down-converted signal; and a seconddemodulator to demodulate the overlay symbols from the down-convertedsignal.

Having described example embodiments of a system and methods forbandwidth efficient phase modulation, it is believed that othermodifications, variations and changes will be suggested to those skilledin the art in view of the teachings set forth herein. It is therefore tobe understood that all such variations, modifications and changes arebelieved to fall within the scope of the present invention as defined bythe appended claims. Although specific terms are employed herein, theyare used in a generic and descriptive sense only and not for purposes oflimitation.

What is claimed is:
 1. A method, comprising: generating a sequence ofphase modulated host symbols having continuous, antipodal phasetransitions between adjacent ones of the host symbols representingdifferent states; receiving a sequence of overlay symbols each spanninga respective set of the host symbols; rotating the continuous, antipodalphase transitions between the adjacent ones of the host symbols in eachset of the host symbols in a same rotation direction according to asymbol state of the respective overlay symbol spanning the set of thehost symbols; and generating a phase modulated transmit signal thatconveys the continuous, antipodal phase transitions rotated according tothe symbol states of the overlay symbols.
 2. The method of claim 1,wherein the rotating includes: rotating the continuous, antipodal phasetransitions in a clockwise direction when the symbol state has a firstvalue; and rotating the continuous, antipodal phase transitions in acounterclockwise direction when the symbol state has an second value. 3.The method of claim 1, further comprising: receiving a host signalincluding a sequence of host signal values; and wherein the generatingthe sequence of phase modulated host symbols includes generating thesequence of phase modulated host symbols from the host signal such thathost symbols represent the host signal values.
 4. The method of claim 1,further comprising: prior to the rotating, patternizing the sequence ofoverlay symbols in accordance with a phase rotation polarity pattern toproduce the sequence of overlay symbols as a patternized sequence ofoverlay symbols, wherein the rotating includes rotating the continuous,antipodal phase transitions in accordance with patternized sequence ofoverlay symbols.
 5. The method of claim 1, wherein the host symbolsinclude non-antipodal phase transitions, the rotating includes rotatingboth the antipodal phase transitions and the non-antipodal phasetransitions in accordance with symbol states of the overlay symbols, andthe generating includes generating the phase modulated transmit signalsuch that the transmit signal conveys the antipodal phase transitionsand the non-antipodal phase transitions rotated according to the symbolstates of the overlay symbols.
 6. An apparatus, comprising: a basebandsignal generator to generate a sequence of phase modulated host symbolshaving continuous, antipodal phase transitions between adjacent ones ofthe host symbols representing different states; a phase rotator toreceive a sequence of overlay symbols each spanning a respective set ofthe host symbols, and to rotate the continuous, antipodal phasetransitions between the adjacent ones of the host symbols in each set ofthe host symbols in a same rotation direction according to a symbolstate of the respective overlay symbol spanning the set of the hostsymbols; and an RF modulator to generate a phase modulated transmitsignal that conveys the continuous, antipodal phase transitions of thephase modulated host symbols rotated according to the symbol states ofthe overlay symbols.
 7. The apparatus of claim 6, wherein the phaserotator is configured to: rotate the continuous, antipodal phasetransitions in a clockwise direction when the symbol state has a firstvalue; and rotate the continuous, antipodal phase transitions in acounterclockwise direction when the symbol state has a second value. 8.The apparatus of claim 6, wherein a phase trajectory of the continuous,antipodal phase transitions extends over an entire host symbol.
 9. Theapparatus of claim 6, wherein a phase trajectory of the continuous,antipodal phase transitions extends over only part of a host symbol. 10.The apparatus of claim 6, wherein the continuous, antipodal phasetransitions have an integrated, Gaussian filtered frequency pulse phasetrajectory.
 11. The apparatus of claim 6, wherein the continuous,antipodal phase transitions have an integrated, raised cosine filteredfrequency-pulse phase trajectory.
 12. The apparatus of claim 6, whereinthe continuous, antipodal phase transitions have a linear phasetrajectory.
 13. The apparatus of claim 6, wherein the continuous,antipodal phase transitions have a continuous phase trajectory.
 14. Theapparatus of claim 6, wherein the host symbols include non-antipodalphase transitions, the phase rotator is configured to rotate both theantipodal phase transitions and the non-antipodal phase transitions inaccordance with symbol states of the overlay symbols, and the RFmodulator is configured to generate the phase modulated transmit signalsuch that the transmit signal conveys the antipodal phase transitionsand the non-antipodal phase transitions rotated according to the symbolstates of the overlay symbols.
 15. The apparatus of claim 14, whereinthe phase rotator is further configured to rotate each non-antipodalphase transition either a long way around a unit circle or a short wayaround the unit circle while transitioning to an adjacent phase state,such that an average direction and speed of a resulting phase rotation,or a cumulative phase shift, over a duration of an overlay symbol isencoded to carry the overlay symbol.
 16. An apparatus, comprising: aradio frequency (RF) front-end to receive an RF signal and frequencydown-convert the RF signal to a down-converted signal, wherein the RFsignal and the down-converted signal each conveys (i) a sequence ofphase modulated host symbols having continuous, antipodal phasetransitions between adjacent host symbols representing different states,and (ii) a sequence of overlay symbols each spanning a respective set ofthe host symbols in time, wherein the continuous, antipodal phasetransitions in each set of the host symbols are rotated in a samedirection according to an overlay symbol state of the respective overlaysymbol spanning the set of host symbols; a first demodulator todemodulate the host symbols from the down-converted signal; and a seconddemodulator to demodulate the overlay symbols from the down-convertedsignal.
 17. The apparatus of claim 16, wherein the second demodulatorincludes a Differential Phase Shift Keying (DPSK) demodulator todemodulate the overlay symbols.
 18. The apparatus of claim 16, whereinthe second demodulator includes a Binary Frequency Shift Keying (BFSK)demodulator to demodulate the overlay symbols.
 19. The apparatus ofclaim 16, the second demodulator is configured to: detect a respectivetotal phase change over each set of host symbols due to the continuous,antipodal phase transitions in the set of the host symbols; anddetermine the symbol state of the overlay symbol spanning the set ofhost symbols based on the detected respective total phase change. 20.The apparatus of claim 19, wherein the total phase change is positive ornegative when the continuous, antipodal phase transitions in the set ofhost symbols are rotated counter-clockwise or clockwise according to thesymbol state of the respective overlay symbol, respectively, and thesecond demodulator is configured to determine the symbol state based onwhether the total phase change is positive or negative.